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Final(Fall06)solutions

# Final(Fall06)solutions - 7 How is the line 2x 29y = 0...

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7. How is the line 2x - 29y = 0 situated with respect to the point (100,7)? (Does it go through the point, abovethe point, or belowthe point?) Clearlyexplainhow you deter- mined your answer. 5% 8. Begin solving the following problems via the Simplex Method ... in each case set up the initial matrix and perform the first pivot - and read off the Basic Feasible Solution after this first pivot. (a) Maximize the function 2x+ 3y subject to the constraints: x + 2y :::;4 - 3x + 2y :::;3 2x -3y :::;2 x 2: 0, y 2: 0 (b) Minimize the function 2x + 3y subject to the constraints: x + 2y 2:4 - 3x + 2y :::;3 2x -3y 2: 2 x 2: 0, y 2: 0 Performjust onepivot in eachcase - and clearly denote the elementary operations that you use,anddon'tforget to readoff theBFS. 15% 9. Below is the feasible region of a 2-D Linear ProgrammingProblem with which I am working (with six comer points and slopesof boundarylines as denoted). The follow- ing fivequestionseach asks you to providean objectivefunction ax + by withparticular properties;in each case, if such an objectivefunctionexists, stateit; if no such objective functionexists,providea clearexplanationof exactlywhynot. E 1) I 0/«. , C 11 0 8 continued ... 3

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